Mark Scheme
Summer 2025
Pearson Edexcel GCSE
In Mathematics
Higher (Non-Calculator) Paper 1H
,Mark Scheme for Edexcel GCSE Mathematics Higher Paper 1
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 23%
• Recurring Patterns:
o Practical scenarios like percentage calculations, proportional reasoning, and
mean/average problems.
o Real-world applications such as cost analysis and recurring decimals.
o Foundational numerical operations integrated with problem-solving tasks.
2. Algebra
• Percentage: 30%
• Recurring Patterns:
o A strong focus on solving equations, simplifying expressions, and
manipulating formulas.
o Recurring themes of sequences, including arithmetic and geometric sequences.
o Multi-step algebraic reasoning tasks requiring careful interpretation and
precision.
3. Geometry
• Percentage: 18%
• Recurring Patterns:
o Problems involving area, volume, and dimensions of 2D and 3D shapes.
o Application of circle theorems, trigonometric calculations, and
transformations.
o Geometry is often integrated with arithmetic or algebra in real-world contexts.
4. Probability and Statistics
• Percentage: 15%
• Recurring Patterns:
o Straightforward probability calculations using Venn diagrams and tree
diagrams.
Page | 2
, o Data interpretation tasks, including histograms, frequency tables, and
averages.
o Testing fundamental understanding of statistical reasoning.
5. Graphs
• Percentage: 11%
• Recurring Patterns:
o Emphasis on interpreting linear and quadratic graphs.
o Tasks focused on graph transformations and plotting key points.
o Limited representation with simpler, more foundational graph-related
problems.
Key Insights Across Papers
1. Most Tested Areas:
• Algebra consistently dominates, accounting for nearly a third of the questions. It
reflects its importance in higher-tier mathematical reasoning.
2. Least Tested Areas:
• Graphs and Probability/Statistics are the least tested topics, focusing on simpler
foundational skills.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
o Many questions are framed in practical scenarios such as budgeting,
population studies, and measurements.
2. Stepwise Progression:
o Tasks often progress from straightforward calculations to complex multi-step
reasoning.
3. Cross-Topic Integration:
o Questions frequently combine concepts, such as integrating geometry with
algebra or arithmetic with probability, testing a holistic understanding of
mathematics.
Page | 3
, Question 1
Here are the first four terms of an arithmetic sequence:
2, 7, 12, 17.
Find an expression, in terms of 𝑛, for the nth term of this sequence. (2 marks)
1. Strategies to Answer the Question
Identify the first term (𝑎1 ):
The first term of the sequence is given as 2. So, 𝑎1 = 2.
Find the common difference:
The common difference (𝑑) is the difference between consecutive terms:
𝑑 = 7 − 2 = 5.
Use the nth term formula for an arithmetic sequence:
The nth term of an arithmetic sequence is given by the formula:
𝑎𝑛 = 𝑎1 + (𝑛 − 1) ⋅ 𝑑.
Substitute the values into the formula:
𝑎𝑛 = 2 + (𝑛 − 1) ⋅ 5.
Simplify the expression:
𝑎𝑛 = 2 + 5𝑛 − 5 = 5𝑛 − 3.
2. Mark Scheme
1. Correctly identify the first term and common difference: 𝑎1 = 2, 𝑑 = 5.
[1 mark]
2. Correctly apply the nth term formula and simplify to get 𝑎𝑛 = 5𝑛 − 3.
[1 mark]
3. Background Theory
Arithmetic Sequences:
• In an arithmetic sequence, the difference between any two consecutive terms is
constant. This is called the common difference (𝑑).
Page | 4
Summer 2025
Pearson Edexcel GCSE
In Mathematics
Higher (Non-Calculator) Paper 1H
,Mark Scheme for Edexcel GCSE Mathematics Higher Paper 1
Five Year Past Paper Question Analysis by topic and frequency
1. Arithmetic
• Percentage: 23%
• Recurring Patterns:
o Practical scenarios like percentage calculations, proportional reasoning, and
mean/average problems.
o Real-world applications such as cost analysis and recurring decimals.
o Foundational numerical operations integrated with problem-solving tasks.
2. Algebra
• Percentage: 30%
• Recurring Patterns:
o A strong focus on solving equations, simplifying expressions, and
manipulating formulas.
o Recurring themes of sequences, including arithmetic and geometric sequences.
o Multi-step algebraic reasoning tasks requiring careful interpretation and
precision.
3. Geometry
• Percentage: 18%
• Recurring Patterns:
o Problems involving area, volume, and dimensions of 2D and 3D shapes.
o Application of circle theorems, trigonometric calculations, and
transformations.
o Geometry is often integrated with arithmetic or algebra in real-world contexts.
4. Probability and Statistics
• Percentage: 15%
• Recurring Patterns:
o Straightforward probability calculations using Venn diagrams and tree
diagrams.
Page | 2
, o Data interpretation tasks, including histograms, frequency tables, and
averages.
o Testing fundamental understanding of statistical reasoning.
5. Graphs
• Percentage: 11%
• Recurring Patterns:
o Emphasis on interpreting linear and quadratic graphs.
o Tasks focused on graph transformations and plotting key points.
o Limited representation with simpler, more foundational graph-related
problems.
Key Insights Across Papers
1. Most Tested Areas:
• Algebra consistently dominates, accounting for nearly a third of the questions. It
reflects its importance in higher-tier mathematical reasoning.
2. Least Tested Areas:
• Graphs and Probability/Statistics are the least tested topics, focusing on simpler
foundational skills.
3. Recurring Patterns Across Papers:
1. Real-Life Contexts:
o Many questions are framed in practical scenarios such as budgeting,
population studies, and measurements.
2. Stepwise Progression:
o Tasks often progress from straightforward calculations to complex multi-step
reasoning.
3. Cross-Topic Integration:
o Questions frequently combine concepts, such as integrating geometry with
algebra or arithmetic with probability, testing a holistic understanding of
mathematics.
Page | 3
, Question 1
Here are the first four terms of an arithmetic sequence:
2, 7, 12, 17.
Find an expression, in terms of 𝑛, for the nth term of this sequence. (2 marks)
1. Strategies to Answer the Question
Identify the first term (𝑎1 ):
The first term of the sequence is given as 2. So, 𝑎1 = 2.
Find the common difference:
The common difference (𝑑) is the difference between consecutive terms:
𝑑 = 7 − 2 = 5.
Use the nth term formula for an arithmetic sequence:
The nth term of an arithmetic sequence is given by the formula:
𝑎𝑛 = 𝑎1 + (𝑛 − 1) ⋅ 𝑑.
Substitute the values into the formula:
𝑎𝑛 = 2 + (𝑛 − 1) ⋅ 5.
Simplify the expression:
𝑎𝑛 = 2 + 5𝑛 − 5 = 5𝑛 − 3.
2. Mark Scheme
1. Correctly identify the first term and common difference: 𝑎1 = 2, 𝑑 = 5.
[1 mark]
2. Correctly apply the nth term formula and simplify to get 𝑎𝑛 = 5𝑛 − 3.
[1 mark]
3. Background Theory
Arithmetic Sequences:
• In an arithmetic sequence, the difference between any two consecutive terms is
constant. This is called the common difference (𝑑).
Page | 4
